Yes, I think so. Intuitively, how I would like to think of this is that we are getting to this from the Euclidean distance metric. But skimming the proof seems

Yes, I think so. Intuitively, how I would like to think of this is that we are getting to this from the Euclidean distance metric. But skimming the proof seems like we use variance (which is defined using squares) as a presupposition.